Analysis And Application Of Two-stage Service Queueing System With Variable System Parameters

The development of unmanned economy has liberated more manpower,and the introduction of intelligent robots has made the service rate of businesses more controllable and has more room for improvement.Based on the fact that the service rate and arrival rate change in real time and the service station has many states,two two-stage queueing models are established.In addition,the unmanned economic operation mode is combined with the queueing model to obtain the optimal parameter values and improve the system efficiency.The main research is as follows:Firstly,from the perspective of customers and businesses,according to the actual situation,the customer’s shopping psychology and the business strategy,a two-stage service queueing model with input rate and service rate changing with the threshold is established.It is assumed that the change of arrival rate in busy period follows a quadratic convex function with fixed parameters,and reaches the maximum value when the customer threshold is m.The changes of the one-stage busy period service rate and the two-stage busy period service rate obey logarithmic function and first-order function respectively.When the customer threshold is n,it starts to increase.The arrival rate during the working vacation period is a quadratic function with a decreasing trend,and the service rate is fixed at this time.The steady-state probability is obtained by the method of matrix geometric solution,and the expression of the performance index is written.The effect of parameters on the model is observed by numerical simulation.In addition,the cost function is established and the optimal parameter values are obtained.Secondly,from the perspective of service station operation,according to the actual situation,the strategies of fault,delayed leave,work leave,ordinary leave,impatient customers and start-up period are combined with the M/M/1/N two-stage queueing model,and the state transition rate matrix of the model is written.The recursive formula of the stationary vector is obtained by iterative and inductive methods.Furthermore,the performance index of the system is written.In addition,the individual and overall benefit functions are established,and the parameter values of the system optimal benefit are obtained by numerical experiments.Finally,taking the unmanned milk tea shop as an example,the data are obtained by field observation,and the hypothesis test method is used to verify that the parameters such as customer arrival time interval and service time interval obey exponential distribution.This data is put into the above queueing model to obtain important performance index values.Finally,the operation mode of the milk tea shop is optimized by establishing a cost function,and the best service rate of the robot is obtained,which improved customer satisfaction and minimized the total cost of the system.